value of integration , Mathematics

Assignment Help:

what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n

Solution)  limit n-->inf.    [1 + (n!-n^n)/n^n]^1/n

= e^ limit n-->inf.    {(n!-n^n)/n^n}.1/n         

                             (applying formula lim x-->a  [1 + f(x)]^g(x) =    e ^ {lim x-->a    f(x).g(x)}  )

=e ^ lim n-->inf.       (n-1)!/(n)^n-1   -   1/n

=e ^ lim n---> inf.     (1-1/n)(1-2/n)(1-3/n)......1/n   -    1/n

=e ^ (1-o)(1-0).....(1-0).0  -   0

=e ^ 0-0

=1

hence, integation 1= x + C

 

 


Related Discussions:- value of integration

Upper limit of normal , Frequently, tests that yield abnormal results are r...

Frequently, tests that yield abnormal results are repeated for confirmation.  What is the probability that for a usual person a test will be at least 1.5 times as high as the upper

Exponents., the (cube square root of 2)^1/2)^3

the (cube square root of 2)^1/2)^3

Algebra, Manuel is a cross-country runner for his school’s team. He jogged ...

Manuel is a cross-country runner for his school’s team. He jogged along the perimeter of a rectangular field at his school. The track is a rectangle that has a length that is 3 tim

Rounding, what is the result if 816.537 is rounded to the nearest tenth

what is the result if 816.537 is rounded to the nearest tenth

Logarithm, I need help with one logarithm problem

I need help with one logarithm problem

Proportions, bananas are on sale for 3 pounds for $2. At that price how man...

bananas are on sale for 3 pounds for $2. At that price how many pounds can you buy for $22

Power series - sequences and series, Power Series We have spent quite...

Power Series We have spent quite a bit of time talking about series now and along with just only a couple of exceptions we've spent most of that time talking about how to fin

Hierarchical structures-how mathematical ideas grow, Hierarchical Structure...

Hierarchical Structures :  As the abstractions from concrete objects and materials become more and more general, they represent wider and wider ideas. If we put down each step of

Reduction-types of word problems related to subtraction, Reduction -when t...

Reduction -when the original amount and the balance or remainder are known, to find the part that has been given away. (e.g., there were 15 toffees in a container, and there are

Graphing formulas, how do you graph y+3=-x+3x on a TI-83 graphing calculato...

how do you graph y+3=-x+3x on a TI-83 graphing calculator?

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd